Abstract
A novel inhomogeneous gauge transformation law is proposed for a non-Abelian adjoint two-form potential in four dimensions. Rules for constructing actions invariant under this are given. The auxiliary vector field which appears in some of these theories transforms like a second connection. Some of the actions also show a local symmetry which is not generated by any local constraint, a novelty for classical field theories. Both types of symmetries change the action by total divergences, suggesting that boundary degrees of freedom have to be taken into account for local quantization.
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